Question

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Length (in mm)	118-126	127-135	136-144	145-153	154-162	163-171	172-180
No. of leaves:	$3$	$5$	$9$	$12$	$5$	$4$	$2$

Find the mean length of leaf.

Answer 1

$Length$	$f_i$	$x_i$	$f_i{x}_i$
$117.5-126.5$	$3$	$122$	$366$
$126.5-135.5$	$5$	$131$	$655$
$135.5-144.5$	$9$	$140$	$1260$
$144.5-153.5$	$12$	$149$	$1788$
$153.5-162.5$	$5$	$158$	$790$
$162.5-171.5$	$4$	$167$	$668$
$171.5-180.5$	$2$	$176$	$352$
	$\sum f_i=40$		$\sum f_i{x}_i=5879$

$\Rightarrow$ $Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{5849}{40}=146.975$